This elderly person has social security and a modest pension. This person with whom she lives can no longer care for her. Is there any hope of getting into a nursing home? So far no one has been able to help.
More information would be helpful here. So these 2 are roommates? How much care was he healthier roommate providing and what has changed now, as in what sort of needs does the elderly person have now that?. You say no one has been able to help, who has been contacted and what answers did they provide? Has APS been contacted? APS or a state social worker should be contacted and the healthier housemate needs to tell the social worker he/she is unable to be responsible for the housemate. Has that been done?
The State will need to take over her care. I would start with Adult protection services. The woman needs to explain she is not related nor can she give the care the woman needs.
At the very least, contact the local department of aging/senior services, police, or even the local city hall. People can direct you to the proper resources.
I would check into board and care homes or assisted living if her situation doesn't require nursing care.
Start by calling your counties council on aging, they can guide you to resources.